Finite Group Databasebeta

← (C2×#261)⋊C32 #16777985

Subgroups — (C2×#261)⋊C32 #16777985

Order 3328.

202 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊C32C211yesmaximal, characteristic
2C2×C16×#261C211yesmaximal, characteristic
3C2×D13×C32C211yesmaximal, characteristic
4C2×C8×#261C411yescharacteristic
5C2×D13⋊C16C411yescharacteristic
6C2×C16×D13C2211yescharacteristic
7C2×#88036C412yescomplemented
8C16×#261—21no—
9C16×#261—21no—
10D13⋊C32—21no—
11D13⋊C32—21no—
12C2×C13×C32C411yescharacteristic, complemented
13C2×#88034C411yescharacteristic, complemented
14D13×C32—21no—
15D13×C32—21no—
16C2×C4×#261C811yescharacteristic
17C2×D13⋊C8C811yescharacteristic
18C2×C8×D13C2×C411yescharacteristic
19C2×#6092C812yes—
20C8×#261—21no—
21C8×#261—21no—
22D13⋊C16—21no—
23D13⋊C16—21no—
24C2×C13×C16C2×C411yescharacteristic
25C2×#6090C2×C411yescharacteristic
26C16×D13D411yescharacteristic
27C16×D13D411yescharacteristic
28C16×D13D411yescharacteristic
29C16×D13Q811yescharacteristic
30#88036—22no—
31C13×C32—21no—
32#88034—21no—
33#7465—131nomaximal, Sylow
34C22×#261C1612yes—
35C2×C4×D13C2×C811yescharacteristic
36C2×#1057C1612yes—
37C4×#261—21no—
38C4×#261—21no—
39D13⋊C8—21no—
40D13⋊C8—21no—
41C2×C8×C13C4211yescharacteristic
42C2×#1055C2×C811yescharacteristic
43C8×D13C22⋊C411yescharacteristic
44C8×D13C4⋊C411yescharacteristic
45C8×D13M1611yescharacteristic
46C8×D13M1611yescharacteristic
47#6092—22no—
48C13×C16C22⋊C411yescharacteristic
49C13×C16C4⋊C411yescharacteristic
50#6090C22⋊C411yescharacteristic
51#6090C4⋊C411yescharacteristic
52C22×C32—131no—
53C22×C32—131no—
54C2×C4×C16—131no—
55C22×D13C2×C1611yescharacteristic
56C2×#261—22no—
57C2×#261—22no—
58C2×#261C3214yescomplemented
59C2×C4×C13C4×C811yescharacteristic
60C2×Dic13C2×C1611yescharacteristic
61C4×D13C22⋊C811yescharacteristic
62C4×D13C4⋊C811yescharacteristic
63C4×D13M3211yescharacteristic
64C4×D13M3211yescharacteristic
65#1057—22no—
66C8×C13#9511yescharacteristic
67C8×C13#9711yescharacteristic
68#1055C22⋊C811yescharacteristic
69#1055C4⋊C811yescharacteristic
70C22×C16—131no—
71C22×C16—131no—
72C2×C4×C8—131no—
73C2×C32—132no—
74C2×C32—131no—
75C2×C32—261no—
76C2×C32—261no—
77C2×C32—261no—
78C2×C32—261no—
79C2×C32#26111yescharacteristic, complemented
80C4×C16—261no—
81C4×C16—261no—
82C22×C13C4×C1611yescharacteristic
83C2×D13C22⋊C1611yescharacteristic
84C2×D13C4⋊C1611yescharacteristic
85C2×D13C2×C3212yes—
86C2×D13M6412yes—
87#261—24no—
88C4×C13#33611yescharacteristic
89C4×C13#34611yescharacteristic
90Dic13C22⋊C1611yescharacteristic
91Dic13C4⋊C1611yescharacteristic
92C22×C8—131no—
93C22×C8—131no—
94C2×C42—131no—
95C2×C16—131no—
96C2×C16—131no—
97C2×C16—131no—
98C2×C16—131no—
99C2×C16—131no—
100C2×C16—132no—
101C2×C16—261no—
102C2×C16—261no—
103C2×C16C2×#26111yescharacteristic
104C4×C8—261no—
105C4×C8—261no—
106C32—21no—
107C32—262no—
108C32—261no—
109C2×C13#137411yescharacteristic
110C2×C13C4×C3211yescharacteristic
111C2×C13#139711yescharacteristic
112D13C22⋊C3212yes—
113D13C4⋊C3212yes—
114C22×C4—131no—
115C22×C4—132no—
116C2×C8—131no—
117C2×C8—131no—
118C2×C8—131no—
119C2×C8—131no—
120C2×C8—131no—
121C2×C8—132no—
122C2×C8—261no—
123C2×C8—261no—
124C2×C8C4×#26111yescharacteristic
125C42—261no—
126C42—261no—
127C16—131no—
128C16—131no—
129C16—262no—
130C16C4⋊#26111yescharacteristic
131C16C22⋊#26111yescharacteristic
132C13#746511yescharacteristic, complemented, Sylow
133C23—131no—
134C2×C4—131no—
135C2×C4—131no—
136C2×C4—131no—
137C2×C4—131no—
138C2×C4—131no—
139C2×C4—134no—
140C2×C4—262no—
141C2×C4—262no—
142C2×C4C8×#26111yescharacteristic
143C8—131no—
144C8—131no—
145C8—262no—
146C8#8810011yescharacteristic
147C8(C2×#261)⋊C411yescharacteristic
148C22—131no—
149C22—131no—
150C22—132no—
151C22—132no—
152C22C16×#26111yescharacteristic
153C4—131no—
154C4—131no—
155C4—264no—
156C4#1171821611yescharacteristic
157C4(C2×#261)⋊C811yescharacteristic
158C2—132no—
159C2—132no—
160C2(C2×#261)⋊C1611yescharacteristic
161C2C32×#26111yescharacteristic
162C2#1312994211yescharacteristic
subgroupG/H
center, FrattiniC2×C16C2×#261
commutatorC2×C13C4×C32
FittingC2×C13×C32C4
socleC22×C13C4×C16
prime radicalC22×D13C2×C16
cosocleC2×C16×D13C22
hypercenterC2×C32#261
hypocenterC13#7465
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C16 ◁ C2×C32

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
7. C2×#88036C4semidirect
12. C2×C13×C32C4semidirect
13. C2×#88034C4semidirect
58. C2×#261C32semidirect
79. C2×C32#261semidirect
132. C13#7465semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D13⋊C322
C2×C16×#2612
C2×D13×C322
#746513